$$\text{Note: Figure not drawn to scale.}$$

In the figure above, line $l$ is prarallel to line $m$. If $x=35$, what is the measure of $\angle ADC$?

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We are given $\angle BAD$. The other angle of $\triangle ABD$ must be complementary.

$$m\angle BDA = 90\degree-m\angle BAD$$ $$35\degree = 90 \degree - \angle BAD$$ $$m\angle BAD = 55 \degree$$

A similar approach is used to find $m\angle BDC$. Since $l$ || $m$, $\overline{BD}$ is perpendicular to line $m$ since is it perpendicular to line $l$. Therefore $m\angle BDC=55 \degree$ since the two angles divided by $\overline{DC}$ must be complementary. $$m\angle ADC = 55\degree + 55\degree$$ $$=\boxed{110 \degree}$$